Measuring Properties of Nanostructure

Atomic structure

To understand a nanomaterial we must first learn about its structure, meaning that we must ascertain the types of atoms that constitute its building blocks, and how their atoms are arranged relative to each other. Most nanostructures are crystalline, meaning that their thousands of atoms have a regular arrangement in space on a crystal lattice.
…..there are 17 possible types of crystal structures called space groups, meaning 17 possible arrangements of atoms in unit cells in two dimensions, and these are divided between the four crystal systems. Of particular interest is the most efficient way to arrange identical atoms on a surface, and this corresponds to the hexagonal system.

In three dimensions the situation is much more complicated. There are seven crystal systems in three dimensions with a total of 230 space groups divided among the systems……the object of a crystal structure analysis is to distinguish the symmetry and space group, to determine the values of the lattice constants and angles, and to identify the positions of the atoms in the unit cell.

There are some special cases of crystal structures that are important for nanocrystals, such as those involving simple cubic (sc), body centered cubic (bcc), and face centered cubic (fcc) unit cells. Another important structural arrangement is formed by stacking planar hexagonal layers, which for a monatomic (single-atom) crystal provides the highest density or closest packed arrangement of identical spheres. If the third layer is placed directly above the first layer, the fourth directly above the second, and so on in A-B-A-B… type sequence, the hexagonal close-packed hcp structure results. If this stacking is carried out by placing the third layer in a third position and the fourth layer above the first, and so forth, the result is an A-B-C-A-B-C-A.. sequence, and the structure is fcc. The latter arrangement is most commonly found in nanocrystals.

Some properties of nanostructures depend on their crystal structure, while other properties such as catalytic reactivity and adsorption energies depend on the type of exposed surface. Epitaxial films prepared from fcc or hcp crystals generally grow with the planar close-packed atomic arrangement. Face centred cubic crystals tend to expose surfaces with this same hexagonal two dimensional atomic array.



Crystallography

To determine the structure of a crystal, and thereby ascertain the positions of its atoms in the lattice, a collimated beam of X rays, electrons, or neutrons is directed at the crystal, and the angles at which the beam is diffracted are measured.....

Each crystallographic plane has three indices h,k,l and for a cubic crystal they are ratios of the points at which the planes intercept the Cartesian coordinate axes x,y,z. the distance d between parallel crystallographic planes with indices hkl for a simple cubic lattice of lattice constant a has the particularly simple form

D = a / (h^2+ k^2+ l^2)

So higher index planes have larger Bragg diffraction angles Ө.



Owen F, Poole C, Nanosolids, Wiley